There are many approaches to removing noise from digital images, however, most methods make use of spatial filtering techniques. One class of noise reduction spatial filters employs a non-linear localized spatial filtering technique directly to a digital image. An example of such a noise reduction filter is the Sigma Filter, described by Jong Sen Lee in the journal article Digital Image Smoothing and the Sigma Filter, Computer Vision, Graphics, and Image Processing Vol. 24, p. 255-269, 1983. This noise reduction filter uses a non-linear pixel averaging technique sampled from a rectangular window about the center pixel. Pixels in a local neighborhood about the center pixel are either included or excluded from the numerical averaging process on the basis of the difference between the local pixel and the center pixel. The small local neighborhood of pixels used by the Sigma filter make it simple to implement and effective at removing the high spatial frequency components of noise.
Gaussian noise sources exhibit random noise fluctuations over a large range of spatial frequencies. Although the Sigma filter was designed to work with Gaussian noise sources, the Sigma filter generally only removes the highest spatial frequency components of noise and thus has difficulty removing the low spatial frequency components of noise. This is largely due to the fact that the Sigma Filter operates on a small local neighborhood of pixels. Therefore, lower spatial frequency components of noise are not removed. The resultant processed digital images with the Sigma filter can have a mottled appearance particularly for sky regions of images that have little image structure.
Multiresolution, or pyramid, methods as a means of representing images as a function of spatial resolution for image processing as a long history. Burt and Adelson, described a method of representing a digital image by a series of residual images and a base digital image in their journal article “The Laplacian Pyramid as a Compact Image Code” IEEE Transactions on Communications, Vol. Com-31, No. 4, April 1983. Although the method taught by Burt and Adelson was designed with image compression methods in mind, the spatial frequency representation has application for noise reduction filtering methods.
Multiresolution, or pyramid-based, noise reduction filters have been used to remove noise from digital images. These methods are designed to remove noise of low and high spatial frequencies. In U.S. Pat. No. 5,729,631 Wober et al. disclose a pyramid spatial frequency decomposition method of removing noise from a digital image using a pyramid of generated with the Discrete Cosine Transform (DCT). This method involves calculating a resolution series of DCT coefficients and a DC image from the original digital image, filtering the DCT coefficients with a Wiener noise filter, and reconstructing the noise reduced digital image. The method taught by Wober et al. removes noise from the digital image for different spatial frequencies by operating on the residual images (DCT coefficients). As such the method taught by Wober et al. cannot be employed without the pyramid construct.
The wavelet spatial frequency decomposition method has also been employed for the use of removing noise from digital images. In U.S. Pat. No. 5,526,446, Adelson and Freeman disclose a technique which converts an image into a set of coefficients in a multi-scale image decomposition process followed by the modification of each coefficient based on its value and the value of coefficients of related orientation, position, or scale. While the method disclosed by Adelson and Freeman is capable of removing noise of low and high spatial frequency, their method must be applied to the set of multi-scale coefficients and cannot be directly applied to a digital image.
Noise in digital images is generally exhibited throughout a range of spatial frequencies. The Sigma filter can be used to remove only the highest spatial frequency components of noise. The methods disclosed by Wober et al. and Adelson et al. can be used to remove the low and high spatial frequency components of noise. However, the class of simple spatial noise filters, such as the Sigma filter, can be applied directly to a digital image while the spatial frequency pyramid-based methods must employ noise filters designed to work with residual images.